1. Field of the Disclosure
The disclosure relates generally to beam combining techniques and, more particularly, to beam combining techniques compatible with high peak power fiber laser applications.
2. Brief Description of Related Technology
In the field of lasers, fiber laser systems enjoy particular interest due to their unique utility in certain applications. Erbium-doped fiber amplifiers (EDFA) are used commercially for long-haul optical communications and other applications that require relatively low power sources. In contrast, Nd-doped fiber lasers (NDFL) and Yb-doped fiber lasers (YDFL) are used in applications demanding high power light sources. Yb-doped fiber lasers are particularly attractive because they offer higher power conversion efficiencies and larger output power levels, due at least in part to their rather simple electron level configuration and efficient photon absorption.
There are numerous applications for high-power fiber lasers, including material processing, remote sensing, and medical applications. Recently, there has been interest in extreme-ultraviolet (EUV) lithography, which is a next-generation lithography technique offering significant reduction in wavelengths compared to current lithography techniques. EUV lithography which uses 13.5 nm wavelengths offers an ability to form much smaller-sized features over current semiconductor design techniques.
Researchers have created some high-power laser-produced-plasma (LPP) EUV sources operating at 13.5 nm. Generally speaking, however, it is difficult to develop a fiber laser source at EUV energies, because the projected power levels needed (˜25 kW) are too great. Some have demonstrated all-fiber-based megawatt (MW) peak-power amplifiers to be feasible candidates for an efficient EUV generation. However, to achieve the required power for a LPP-EUV-source, as would be required for lithography stepper machines, multiple laser beams would have to be combined using what are called beam combining techniques.
Current laser beam combining techniques include technologies using spectral beam combining (SBC) and coherent beam combining (CBC). State of the art beam combining systems, for example, have been shown to produce a combined power of 522 W using SBC and combined power of 470 W using CBC. Between the two, the SBC technique appears to be most desired due to perceived robustness and relative simplicity of implementation.
Current SBC techniques, however, are based on spatial-spectral-dispersion combining-elements, i.e., diffraction gratings, that superimpose beams of different optical wavelengths to form the combined, high-power beam. For these types of combining-elements, there exists a limitation on laser spectral-width and beam-size that must be maintained to retain sufficient mode quality on a combined-beam. This limitation is a principal problem for fiber-lasers with MW-peak-power due to nonlinear-induced spectral-broadening. Beyond these spectral-width and beam size limitations, existing grating-based combining-elements are unable to withstand operation at optical powers of 25 kW, because of thermal-induced wave-front distortion at such high power levels.
As noted above, one limitation of conventional spectral combining techniques is the inherent trade-off between signal spectral width on each laser channel and the maximum allowable beam size on the combining element. This trade-off fundamentally originates in the fact that a finite spectral linewidth corresponds to a finite amount of the spectral divergence of the signal beam at the output of the combining element. Since divergence of an optical beam due to diffraction is inversely proportional to the beam spot size, the combined beam should have a spot size that is small enough such that beam divergence resulting from diffraction dominates over the beam divergence resulting from spatial spectral dispersion. That is, the combined beam should have a spot size such that the quality of the laser beam is not affected by spatial spectral dispersion. For a diffraction grating this trade-off between the allowable beam spot size is expressed as:
                              Δλ          ·                      ω            0                          =                              2            ⁢                                                                                                      (                                              M                        2                                            )                                        2                                    -                  1                                            ·              c              ·                              cos                ⁡                                  (                                      α                    0                                    )                                                                          g            ⁢                                                  ⁢            λπ                                              (        1        )            where Δλ is the linewidth in Hz, ω0 is the beam width in mm, M2 is the beam quality of the combined output beam (diffraction-limited beams incident onto the grating are assumed), c is the speed of light, α0 is the incident angle of the grating (usually equal to the Littrow angle), and g is the grating groove density in lines/mm.
FIG. 1(a) illustrates the tradeoff between linewidth and beam width for a near-diffraction-limited output beam (M2=1.2˜1.5) using a diffraction grating combiner with a 1064 nm wavelength, 1740 lines/mm grating and a Littrow angle ˜66°, which are the same parameters as typically used for SBC.
The general practical constraint that this trade-off imposes on a fiber laser based spectral-combining system is two-fold. First, because each laser channel has to operate within a very narrow spectral linewidth, spectral broadening due to fiber nonlinearities (e.g., stimulated Brillouin scattering (SBS) for continuous wave (cw) signals or self-phase modulation (SPM) for pulsed signals) severely restricts the power one can achieve per laser channel. Second, because the beam spot size on a combining grating is limited, the potential for high thermal loading and optical grating damage limits the total combined power that one can achieve. Overcoming these constraints would require use of a very large number of laser channels, as well as the development of new grating technologies that are resistant to very high optical power densities.
Pulsed laser applications are particularly limited because of the spectral broadening that results from SPM. This SPM induced broadening severely limits spectral linewidths that could be made available for a multi-stage MW-peak-power Yb-doped fiber amplifier. Assuming a bandwidth-limited Gaussian pulse injected into a cascaded n-stage fiber amplifier system, where each stage is characterized by a different gain, core size and length, one can express the overall spectral broadening (δωmax) in the system as:
                              δω          max                =                              ∑                          i              =              1                        n                    ⁢                      0.86            ⁢                          T              0                              -                1                                      ⁢                                          2                ⁢                π                ⁢                                                                  ⁢                                  n                  2                                                            λ                ⁢                                                                  ⁢                                  A                                      eff                    ⁡                                          (                      i                      )                                                                                            ⁢                          P              i                        ⁢                                          1                -                                  exp                  ⁡                                      (                                                                  g                        i                                            ⁢                                              L                        i                                                              )                                                                              g                i                                                                        (        2        )            where n is the number of amplifier stages, T0 is the initial pulse duration, n2 is the nonlinear refractive index (3.2×10−20 m2/W for fused silica), λ is the wavelength of the signal, and Aeff(i), Pi, gi and Li are the effective core area, input peak power, gain and length for the i-th amplification stage, respectively. As an example, consider a high peak power narrow-linewidth pulsed system using a 100 μm core photonic-crystal rod waveguide as the last amplification stage (see, e.g., Brooks and Teodoro, “Multinnegawatt peak-power, single-transverse-mode operation of a 100 μm core diameter. Yb-doped rodlike photonic crystal fiber amplifier,” Appl. Phys. Lett. 89, 111119 (2006)). Such a large core significantly exceeds the fiber core sizes achieved in practical fiber lasers, and, therefore, provides an upper-limit estimate for detrimental nonlinear effects in a pulsed fiber amplifier. With the system architecture and parameters provided by Brooks and Teodoro, “Multimegawatt peak-power, single-transverse-mode operation of a 100 μm core diameter, Yb-doped rodlike photonic crystal fiber amplifier,” and assuming equal gain for each stage with 3 dB of inter-stage loss (due to the optical isolators, filters and coupling losses) Expression (2) gives ˜18 GHz of SPM-induced spectral broadening for MW peak power and 1 ns duration pulses at the system output. This is consistent with the experimental data reported. For longer pulse durations SPM is no longer the dominant nonlinearity. Instead, our analysis and experimental data indicates that for pulse durations of a few nanoseconds and longer, four-wave-mixing and stimulated Raman scattering become the limiting factors, not SPM.
In any event, this analysis demonstrates that even using the maximum-size fiber cores extraction of the highest (MW peak) power pulses results in a minimum spectral width of an amplified signal in the range of 10's of GHz or larger. FIG. 1a shows that for lasers with tens of GHz of linewidth, a beam radius less than 1 mm is required, which would result in a very high power density on a combining grating. In particular, FIG. 1a shows that for such linewidths to achieve a diffraction-limited (M2<1.2) combined beam requires a spot size diameter on the combining grating to be in the range of 2-3 mm or smaller. With that beam size, one can only combine up to ˜25 mJ of ns-pulses by gold-coated gratings, given their reported damage threshold of ˜0.8 J/cm2 for 1-ns pulses. Dielectric diffraction-gratings have a higher damage threshold, up to 4.4 J/cm2 for 5-ns pulses, giving a maximum combined energy ˜138 mJ. However, the power density even for a 5-kW combined power can reach ˜160 kW/cm2 on the dielectric grating, and this power density will lead to waveform distortion. FIG. 1b plots the power density as a function of the beam radius for the targeted combining power 5 kW, 25 kW and 100 kW (with Littrow incident angle). The plots provide a power density of ˜1294 kWm/cm2 for 100 kW with a 1 mm radius beam, for example. These intensity levels will create thermal-induced wavefront distortion, and very likely, thermal damage on conventional grating-based beam combining systems.
In light of the limitations with conventional schemes, spectral combining schemes that operate without spatial-spectral-dispersion are desirable, especially if one hopes to use beam combining techniques with fiber-lasers capable of producing MW peak-power and multi-kW of average power.